Mandyam V. Srinivasan

Predictive coding: a fresh view of inhibition in the retina

Interneurons exhibiting centre-surround antagonism within their receptive fields are commonly found in peripheral visual pathways. We propose that this organization enables the visual system to encode spatial detail in a manner that minimizes the deleterious effects of intrinsic noise, by exploiting the spatial correlation that exists within natural scenes. The antagonistic surround takes a weighted mean of the signals in neighbouring receptors to generate a statistical prediction of the signal at the centre. The predicted value is subtracted from the actual centre signal, thus minimizing the range of outputs transmitted by the centre. In this way the entire dynamic range of the interneuron can be devoted to encoding a small range of intensities, thus rendering fine detail detectable against intrinsic noise injected at later stages in processing. This predictive encoding scheme also reduces spatial redundancy, thereby enabling the array of interneurons to transmit a larger number of distinguishable images, taking into account the expected structure of the visual world. The profile of the required inhibitory field is derived from statistical estimation theory. This profile depends strongly upon the signal: noise ratio and weakly upon the extent of lateral spatial correlation. The receptive fields that are quantitatively predicted by the theory resemble those of X-type retinal ganglion cells and show that the inhibitory surround should become weaker and more diffuse at low intensities. The latter property is unequivocally demonstrated in the first-order interneurons of the fly’s compound eye. The theory is extended to the time domain to account for the phasic responses of fly interneurons. These comparisons suggest that, in the early stages of processing, the visual system is concerned primarily with coding the visual image to protect against subsequent intrinsic noise, rather than with reconstructing the scene or extracting specific features from it. The treatment emphasizes that a neuron’s dynamic range should be matched to both its receptive field and the statistical properties of the visual pattern expected within this field. Finally, the analysis is synthetic because it is an extension of the background suppression hypothesis (Barlow & Levick 1976), satisfies the redundancy reduction hypothesis (Barlow 1961 a, b) and is equivalent to deblurring under certain conditions (Ratliff 1965).

The concepts of 'sameness' and 'difference' in an insect

Insects process and learn information flexibly to adapt to their environment. The honeybee Apis mellifera constitutes a traditional model for studying learning and memory at behavioural, cellular and molecular levels. Earlier studies focused on elementary associative and non-associative forms of learning determined by either olfactory conditioning of the proboscis extension reflex or the learning of visual stimuli in an operant context. However, research has indicated that bees are capable of cognitive performances that were thought to occur only in some vertebrate species. For example, honeybees can interpolate visual information, exhibit associative recall, categorize visual information and learn contextual information. Here we show that honeybees can form ‘sameness’ and ‘difference’ concepts. They learn to solve ‘delayed matching-to-sample’ tasks, in which they are required to respond to a matching stimulus, and ‘delayed non-matching-to-sample’ tasks, in which they are required to respond to a different stimulus; they can also transfer the learned rules to new stimuli of the same or a different sensory modality. Thus, not only can bees learn specific objects and their physical parameters, but they can also master abstract inter-relationships, such as sameness and difference.

Searching behaviour of desert ants, genusCataglyphis (Formicidae, Hymenoptera)

Summary1.If a homing ant (Cataglyphis bicolor,C. albicans) gets lost, it does not perform a random walk but adopts a stereotyped search strategy. During its search the ant performs a number of loops of ever-increasing size, starting and ending at the origin and pointing at different azimuthal directions. This strategy ensures that the centre area where the nest is most likely to be, is investigated most extensively.2.After one hour of continuous search the ants search paths cover an area of about 104 m2. Nevertheless, the system of loops performed during this time is precisely centred around the origin. The ants searching density does not depend on the azimuthal direction around the origin but only on the distance from the origin. It rapidly decreases with increasing distance.3.The ants searching pattern can be characterized by two functions: thed/t-function correlating distance (d) with time (t), and theα/t-function correlating azimuthal direction (α) with time. If fixes of the ants position are taken every 10 s, the vectors pointing from the origin to successive fixes change their lengthsd systematically (α/t-function) and their directionsα randomly (α/t-function). What is especially characteristic of the ants searching pattern is the oscillatingd/t-function which clearly demonstrates that the searching ant repeatedly returns to the origin, even after it has walked, within one hour, along a search trajectory of more than 1 km (the latter number refers toC. albicans-A). The ants walking speed does not change within a search time of 1 h.4.The distribution of changes in direction between successive segments of a search path,β, is usually unimodal with a mean of 0°, if complete search paths are considered. Nevertheless, within smaller periods of time, especially during the initial portions of the search the integrated angleβ may continuously change in the same direction. Such portions of the search crudely resemble a spiral which alternately expands and contracts.5.Although all 3 species ofCataglyphis studied in this paper adopt the same general search strategy, there are some differences in the fine structure of the search:C. albicans-A departs further from the origin than any other species, and performs the most rapid turns. The tendency towards spiralling is most pronounced inC. albicans-B.6.An efficient searching strategy is formulated, based on purely theoretical grounds. It is assumed that when the search begins the probability density function (PDF) for the location of the nest is Gaussian in two dimensions (a priori PDF). It is further assumed that the ant can never becompletely certain that a given area has been fully explored, so that it is only theprobability of encountering the nest within a certain region that decreases as the time spent in searching this region increases. Thus, the most promising region to search is specified by an a posteriori PDF which takes the ants past performance into account.7.A computer model is presented that searches in optimum fashion, as proposed above. In the model, motion of the ant is characterized in terms of radial and tangential components, with the tangential component varying randomly and the radial component varying according to the a posteriori PDF. The model successfully describes what the ants are actually doing (e.g., compare Figs. 17 and 18 with Fig. 3, Figs. 19 and 20 with Figs. 8–10, and Fig. 21a and b with Figs. 4 and 5), indicating that the searching behaviour ofCataglyphis is geared to find the nest as quickly as possible.

Reflective surfaces for panoramic imaging

A family of reflective surfaces is presented that, when imaged by a camera, can capture a global view of the visual environment. By using these surfaces in conjunction with conventional imaging devices, it is possible to produce fields of view in excess of 180 degrees that are not affected by the distortions and aberrations found in refractive wide-angle imaging devices. By solving a differential equation expressing the camera viewing angle as a function of the angle of incidence on a reflective surface, a family of appropriate surfaces has been derived. The surfaces preserve a linear relationship between the angle of incidence of light onto the surface and the angle of reflection onto the imaging device, as does a normal mirror. However, the gradient of this linear relationship can be varied as desired to produce a larger or smaller field of view. The resulting family of surfaces has a number of applications in surveillance and machine vision.

Pattern recognition in bees: orientation discrimination

Summary1.Honey bees (Apis mellifera, worker) were trained to discriminate between two random gratings oriented perpendicularly to each other. This task was quickly learned with vertical, horizontal, and oblique gratings. After being trained on perpendicularly-oriented random gratings, bees could discriminate between other perpendicularly-oriented patterns (black bars, white bars, thin lines, edges, spatial sinusoids, broken bars) as well.2.Several tests indicate that the stimuli were not discriminated on the basis of a literal image (eidetic template), but, rather, on the basis of orientation as a single parameter. An attempt to train bees to discriminate between two different random gratings oriented in the same direction was not successful, also indicating that the bees were not able to form a template of random gratings.3.Preliminary experiments with oriented ‘Kanizsa rectangles’ (analogue of Kanizsa triangle) suggest that edge detection in the bee may involve mechanisms similar to those that lead to the percept of illusory contours in humans.

How honeybees make grazing landings on flat surfaces.

Abstract. Freely flying bees were filmed as they landed on a flat, horizontal surface, to investigate the underlying visuomotor control strategies. The results reveal that (1) landing bees approach the surface at a relatively shallow descent angle; (2) they tend to hold the angular velocity of the image of the surface constant as they approach it; and (3) the instantaneous speed of descent is proportional to the instantaneous forward speed. These characteristics reflect a surprisingly simple and effective strategy for achieving a smooth landing, by which the forward and descent speeds are automatically reduced as the surface is approached and are both close to zero at touchdown. No explicit knowledge of flight speed or height above the ground is necessary. A model of the control scheme is developed and its predictions are verified. It is also shown that, during landing, the bee decelerates continuously and in such a way as to keep the projected time to touchdown constant as the surface is approached. The feasibility of this landing strategy is demonstrated by implementation in a robotic gantry equipped with vision.

Evidence for counting in insects

Here we investigate the counting ability in honeybees by training them to receive a food reward after they have passed a specific number of landmarks. The distance to the food reward is varied frequently and randomly, whilst keeping the number of intervening landmarks constant. Thus, the bees cannot identify the food reward in terms of its distance from the hive. We find that bees can count up to four objects, when they are encountered sequentially during flight. Furthermore, bees trained in this way are able count novel objects, which they have never previously encountered, thus demonstrating that they are capable of object-independent counting. A further experiment reveals that the counting ability that the bees display in our experiments is primarily sequential in nature. It appears that bees can navigate to food sources by maintaining a running count of prominent landmarks that are passed en route, provided this number does not exceed four.

Robot navigation inspired by principles of insect vision

Abstract Recent studies of insect visual behaviour and navigation reveal a number of elegant strategies that can be profitably applied to the design of autonomous robots. The peering behaviour of grasshoppers, for example, has inspired the design of new rangefinding systems. The centring response of bees flying through a tunnel has led to simple methods for navigating through corridors. Experimental investigation of the bees “odometer” has led to the implementation of schemes for visually driven odometry. These and other visually mediated insect behaviours are described along with a number of applications to robot navigation.

Motion detection in insect orientation and navigation

The visual systems of insects are exquisitely sensitive to motion. Over the past 40 years or so, motion processing in insects has been studied and characterised primarily through the optomotor response. This response, which is a turning response evoked by the apparent movement of the visual environment, serves to stabilise the insects orientation with respect to the environment. Research over the past decade, however, is beginning to reveal the existence of a variety of other behavioural responses in insects, that use motion information in different ways. Here we review some of the recently characterised behaviours, describe the inferred properties of the underlying movement-detecting processes, and propose modified or new models to account for them.

Honey Bees as a Model for Vision, Perception, and Cognition

Among the so-called simpler organisms, the honey bee is one of the few examples of an animal with a highly evolved social structure, a rich behavioral repertoire, an exquisite navigational system, an elaborate communication system, and an extraordinary ability to learn colors, shapes, fragrances, and navigational routes quickly and accurately. This review examines vision and complex visually mediated behavior in the honey bee, outlining the structure and function of the compound eyes, the perception and discrimination of colors and shapes, the learning of complex tasks, the ability to establish and exploit complex associations, and the capacity to abstract general principles from a task and apply them to tackle novel situations. All this is accomplished by a brain that weighs less than a milligram and carries fewer than a million neurons, thus making the bee a promising subject in which to study a variety of fundamental questions about behavior and brain function.